I've been gone for a while but now that I'm back I noticed that there are hearts under the avatars in the forums? One next to 'avatar' and one next to 'post'. What do they mean?

One is to like the post and the other is to like the avatar. :) The total likes for the avatar for you as a user is in your user dashboard (hover over personal first to get there).

You can click the heart that says Avatar to "like" a person's avatar. The other is to "like" a post. Last I knew you could like up to 25 HAs a day. I don't know if there are limits for liking posts.

You can check your avatar likes under preferences.

Not sure what effects liking a post does. I think it only tracks it for a day, then goes away.

Thank you, :) Are there achievements for these likes or anything like that?

Thank you for your response as well, :)

There aren't (at the moment). There haven't been any new achievements added in a while because apparently they're 'broken' or something. There might be some added for them in the future, maybe. :)